Field of the Invention
[0001] The present invention relates to communication of digital signals, more particularly
to a method and a device for transmission and/or reception of digital signals using
diversity (e.g. Multiple Description Coding - MDC) to overcome channel impairments,
as well as to the signals themselves and a network for transmitting and receiving
the signals
Technical Background
[0002] A new family of communication services involving the delivery of image data over
bandwidth limited and error prone channels as packet networks and wireless links has
emerged in the last few years In order to increase the reliability over these types
of channels, diversity is commonly resorted to, besides error correction techniques.
Multiple Description Coding (MDC) has been introduced to efficiently overcome channel
impairments over diversity-based systems allowing decoders to extract meaningful information
from a subset of a bit-stream
[0003] In his PhD Thesis, which can be found in electronic format on
http.//lcavwww.epfl.ch/∼goyal/Thesis/, Vivek K Goyal offers an overview of MDC in general and achievable rate-distortion
regions. The focus of previous research was laid on finding the optimal achievable
rate-distortion regions and their boundaries, as described in L Ozarow, "On a source
coding problem with two channels and tree receivers,"
Bell Syst. Tech. J., vol. 59, pp 1909-1921, 1980, and in A. A El Gamal and T. M. Cover, "Achievable rates
for multiple descriptions,"
IEEE Trans. Inform. Th., vol IT-28, no. 6, pp 851-857, 1982 This is followed by the design of practical compression
systems to meet these theoretical boundaries. Examples include methods based on quantization
as described in V A. Vaishampayan, "Design of multiple description scalar quantizers,"
IEEE Trans. Inform. Th., vol. 39, no. 3, pp. 821 - 834, 1993, and in V. A. Vaishampayan and J Domaszewicz,
"Design of entropy-constrained multiple description scalar quantizers,"
IEEE Trans. Inform. Theory, vol. 40, no. 1, pp. 245-250, 1994, and methods based on multiple description transform
as described in J. Batllo and V. Vaishampayan, "Asymptotic performance of multiple
description transform codes,"
IEEE Trans. Inform. Theory, vol. 43, no. 2, pp. 703-707, 1997, and in V. Goyal, J. Kovacevic, R Arean, and M
Vetterli, "Multiple description transform coding of images,"
Proc. IEEE Int. Conf. Image Proc. ICIP'98, pp. 674-678, 1998. A design of Multiple Description Scalar Quantizers (MDSQ)
is pioneered in V. A. Vaishampayan, "Design of multiple description scalar quantizers,"
IEEE Trans. Inform. Th., vol. 39, no. 3, pp. 821 - 834, 1993 under an assumption of fixed length codes and
fixed codebook sizes. Significant improvements are achieved in V. A. Vaishampayan
and J. Domaszewicz, "Design of entropy-constrained multiple description scalar quantizers,"
IEEE Trans. Inform. Theory, vol. 40, no. 1, pp 245-250, 1994 where the design of the quantizers is subject to
the constraint of a given entropy, and not of a given codebook size
[0004] In order to achieve robust communication over unreliable channels the MDC system
has to deliver highly error-resilient bit-streams characterised by a corresponding
high level of redundancy. Additionally, a fine grain scalability of the bit-stream
is a desirable feature for bandwidth varying channels. A system conceived so as to
meet these requirements is described in T. Guionnet, C. Guillemot, and S. Pateux,
"Embedded multiple description coding for progressive image transmission over unreliable
channels,"
Proc. IEEE Int. Conf. Image Proc., ICIP 2001, pp. 94 - 97, 2001, where a progressive MDC algorithm is based on Multiple
Description Uniform Scalar Quantizers (MDUSQ). Moreover, for a high level of redundancy
and for low bit-rates, the approach of this document outperforms the embedded MDC
algorithm based on a polyphase transform as proposed in W. Jiang and A. Ortega, "Multiple
description coding via polyphase transform and selective quantization,"
Proc. SPIE Int. Conf. Visual Comm. Image Proc., VCIP'99, San Jose, USA, pp. 998-1008, 1999.
[0005] The system proposed in V. A. Vaishampayan, "Design of multiple description scalar
quantizers,"
IEEE Trans. Inform. Th., vol. 39, no. 3, pp. 821 - 834, 1993, relies on the ability to design scalar quantizers
with nested thresholds. A source signal or input signal, generally called "a source",
represented by a random process
{Xn, n ∈ Z+ with zero mean and variance σ
is quantized by side quantizers
Q:R→ {0,1,...,K-1 },
m being a value between 1 and the number of side quantizers available, for example
m = 1, 2, and K being the number of quantization intervals of a side quantizer for
a quantization level. In the example given with two side quantizers, each of the two
quantizers outputs an index q
,k∈Z
+ for a quantization level, which indexes can be separately used to estimate the source
sample. A reconstruction where
Q(x)=
q must be the centroid of the cell or quantization interval
Q(
q). If both indices
Q(
x)=
q and
Q(x)=
q are received, the reconstruction is the centroid of the intersection
Q(
q,
q)=
Q(
q)t
Q(
q) represented by the central inverse quantizer. The number of diagonals covered in
the index assignment matrix triggers the redundancy between the two descriptions,
as described in V. A. Vaishampayan, "Design of multiple description scalar quantizers,"
IEEE Trans. Inform. Th., vol. 39, no. 3, pp. 821 - 834, 1993.
[0006] Quantization methods based on embedded scalar quantizers are previously proposed
in the literature - see for e.g. D. Taubman and M. W Marcellin,
JPEG2000 - Image Compression: Fundamentals, Standards and Practice. Hingham, MA: Kluwer Academic Publishers, 2001. In embedded quantization, the partition
cells or quantization intervals at higher quantization rates are embedded in the quantization
intervals at lower rates. A quantization rate relates to the number of quantization
intervals at a quantization level. A set of embedded side quantizers
Q,
Q, ... ,
Q with m=1,2 the number of side quantizers, and P+1 the number of quantization levels,
and a set of embedded central quantizers
Q,
Q,
Q where
Q (
q,
q)=
Q (
q)I
Q(
q) for any quantization level
p, 0 ≤
p ≤ P are assumed. The number of quantization levels may be freely selected e g. seven
or more or ten or more levels. The quantization intervals of any quantizer
Q and
Q are embedded in the quantization intervals of the quantizers
Q,
Q,...,
Q and
Q,
Q,...,
Q respectively. It is considered that the quantizer at level
p (e.g.
Q is finer than the quantizer at level
p +1 (e. g.
Q) if at least one of the quantization intervals of the quantizer at level
p+1 is split into at least two quantization intervals at level p .
[0007] The number of side quantization intervals of the lowest-rate quantizer
Q is denoted by
N and the number of quantization intervals in which an arbitrary side quantization
interval
S of
Q is divided is denoted by
Lk The maximum number of intervals in which any side quantization interval
S is partitioned over all quantization levels is denoted by
Np, with
Lk ≤ Np for any k. Starting from the lowest-rate quantizer
Q each side quantization interval
S, 0 ≤
kp ≤
N is divided into a number of
Lkp quantization intervals
S, 0 ≤
kP-1 <
Lkp of
Q. In general, for each side-quantizer
Q one associates to any
x ∈ S, the quantizer index
kp,
kP-1, ...kp. This allows to obtain the indices of lower rate quantization by leaving aside components
of higher rate quantization, similar to the uniform embedded scalar quantizers as
described in D. Taubman and M W. Marcellin,
JPEG2000 - Image Compression: Fundamentals, Standards and Practice. Hingham, MA: Kluwer Academic Publishers, 2001.
Summary of the Invention
[0008] The present invention aims at providing a method and device for robust progressive
image transmission of encoded digital signals over unreliable channels with variable
bandwidth which yield a better rate-distortion performance compared to known Multiple
Description Uniform Scalar Quantizers (MDUSQ) The signals may correspond to detectable
physical quantities, such as, but not limited to, pressures, voltages, magnetic field
strengths, photon energies and counts, that capture conditions at a particular time
and place Communication or transmission of those signals allows for sight and sound
reproduction. According to the present invention, a type of embedded scalar quantizers
for Multiple Description Coding (MDC) systems are introduced, which are referred to
as Embedded Multiple Description Scalar Quantizers (EMDSQ) hereinafter.
[0009] In one aspect the present invention provides an Embedded Multiple Description Scalar
Quantizer (EMDSQ) which provides a fine-grain refinable representation of the input
data and are designed, for example, under the constraint of producing double-deadzone
central quantizers at each quantization level. The term double deadzone is usually
used with uniform quantizers to indicate that the size of the central partition about
zero is equal to the double of the size of the other partitions. In accordance with
the present invention, non-uniform partitioning can be used and the term double deadzone
is extended to include central partitions so that the double deadzone is within 1.5
to 2.5 times the other partitions. Moreover, in accordance with another aspect of
the present invention, a control mechanism for the EMDSQ is provided which allows
for tuning the descriptions' redundancy for each quantization level. The employed
mechanism enables:
(1) to control the tradeoff between coding efficiency and resilience to errors, and
(2) to improve the resilience by increasing the redundancy in the important layers
of the bit-streams thus resulting in improved experimental results.
[0010] In a further aspect the control mechanism allows for tuning the redundancy between
the two or more descriptions for each quantization level. The employed mechanism enables
the control of the tradeoff between the coding efficiency and error-resilience, and
provides an increased robustness by improving the error resilience in the most important
layers of the embedded bit-streams. Instantiations of the proposed family, for example
can be incorporated in a wavelet-based embedded coding system having a redundancy-control
mechanism.
[0011] The EMDSQ of the present invention meet features desired for robust progressive image
transmission over unreliable channels, such as for example a high redundancy level,
fine grain rate adaptation and progressive transmission of each description. For an
erasure channel model characterised by burst errors, progressive transmission also
provides quality improvement for the central reconstruction due to the use of undamaged
data from partially damaged received side channels. The reconstruction of the central
channel can be performed if the receiver knows where the burst error occurs. To satisfy
this requirement, techniques such as inserting synchronisation markers in the bit-stream
can be used.
[0012] The EMDSQ of the present invention may be incorporated in any suitable coding system
such as a DCT coding or, for example, a wavelet-based coding system that employs a
Quad Tree (QT) coding algorithm as described in A. Munteanu, J. Comelis, G. Van der
Auwera, and P. Cristea, "Wavelet-based lossless compression scheme with progressive
transmission capability,"
Int. J. Imaging Systems and Tech., vol. 10, no. 1, pp 76-85, Jan. 1999
[0013] The present invention provides a method for transmitting a digital signal, the method
comprising quantizing a source digital signal to generate with different quantizations
at least a first and a second bit-stream, of which at least one bit-stream has been
generated by an embedded quantization, transmitting at least one of the at least first
and second bit-streams and generating a dequantized digital signal from at least parts
of one of the transmitted at least first and second bit streams, whereby if in the
generation of the dequantized digital signal the parts of the at least first and second
bit-streams are combined, the combined dequantized signal is generated by an embedded
dequantizer having at least two quantization levels and having at least one quantization
interval at each quantization level which is finer than quantization intervals for
dequantizing any of the at least first and second bit-streams.
[0014] Each quantization level has a quantization rate. A quantization rate corresponds
to the number of quantization intervals a digital signal is divided into at a certain
quantization level. At least one bit-stream generated by an embedded quantization
may be generated by an embedded quantization where at least two quantization intervals
at lower quantization rate are split into a different number of quantization intervals
at higher quantization rate At least one bit-stream generated by an embedded quantization
may be generated by a non-uniform embedded quantization At least one bit-stream generated
by a non-uniform embedded quantization may be generated by a non-uniform embedded
dead zone quantization. At least one bit-stream generated by a non-uniform embedded
dead zone quantization is generated by a non-uniform embedded double dead zone quantization.
[0015] Alternatively, at least one bit-stream generated by an embedded quantization may
be generated by a uniform embedded quantization. At least one bit-stream generated
by a uniform embedded quantization may be generated by a uniform embedded dead zone
quantization. At least one bit-stream generated by a uniform embedded dead zone quantization
may be generated by a uniform embedded double dead zone quantization.
[0016] Instead of one or more bit-streams, each bit-stream may be generated by an embedded
quantization.
[0017] A method according to the present invention may furthermore comprise selecting end
points of quantization intervals of a quantizer such that at least one of the end
points does not coincide with end points of a quantization interval of another quantizer.
The embedded quantization may comprise at least three levels, preferably more than
seven levels, and still more preferred more than ten levels The quantizing of the
source digital signal may comprise an embedded successive approximation quantization
at every quantization level
[0018] The present invention also provides a device for transmitting a digital signal. The
device comprises a quantizing means for quantizing a source digital signal to generate
with different quantizations at least a first and a second bit-stream, of which at
least one bit-stream has been generated by an embedded quantization, and transmitting
means for transmitting at least one of the at least first and second bit-streams.
The quantizing means are such that when a dequantized digital signal is generated
from at least parts of one of the transmitted at least first and second bit streams,
if in the generation of the dequantized digital signal the parts of the at least first
and second bit-streams are combined, the combined dequantized signal is generated
by an embedded dequantizer having at least two quantization levels and having at least
one quantization interval at each quantization level which is finer than quantization
intervals for dequantizing any of the at least first and second bit-streams.
[0019] At least one bit-stream generated by an embedded quantization may be generated by
an embedded quantizer where at least two quantization intervals at lower quantization
rate are split in a different number of quantization intervals at higher quantization
rate. At least one bit-stream generated by an embedded quantizer may be generated
by a non-uniform embedded quantizer. At least one bit-stream generated by a non-uniform
embedded quantizer may be generated by a non-uniform embedded dead zone quantizer.
At least one bit-stream generated by a non-uniform embedded dead zone quantizer may
be generated by a non-uniform embedded double dead zone quantizer.
[0020] Alternatively, a device according to the present invention may be such that at least
one bit-stream generated by an embedded quantizer is generated by a uniform embedded
quantizer. At least one bit-stream generated by a uniform embedded quantizer may be
generated by a uniform embedded dead zone quantizer. At least one bit-stream generated
by a uniform embedded dead zone quantizer may be generated by a uniform embedded double
dead zone quantizer
[0021] Each bit-stream may be generated by an embedded quantizer.
[0022] The quantizing means may include means for selecting end points of quantization intervals
of a quantization such that at least one of the end points does not coincide with
end points of a quantization interval of another quantizer
[0023] The embedded quantization may comprise at least three levels, preferably more than
seven levels, and still more preferred more than ten levels.
[0024] The quantizing means may comprise an embedded successive approximation quantizer
for carrying out an embedded successive approximation quantization at every quantization
level
[0025] A device according to the present invention may be located in a node of a telecommunications
network.
[0026] The present invention also provides a device for receiving a digital signal. The
device comprises receiving means for receiving at least a first and a second bit-stream,
and dequantizing means for generating a dequantized digital signal from the received
first and second bit-streams. The dequantizing means comprise combining means for
combining, in the generation of the dequantized digital signal, the at least first
and second bit-streams, the combined dequantized signal being generated by an embedded
dequantizer having at least two quantization levels and having at least one quantization
interval at each quantization level which is finer than quantization intervals for
dequantizing any of the at least first and second bit-streams.
[0027] At least one of the first and the second bit-streams may be generated by an embedded
quantizer where at least two quantization intervals at lower quantization rate are
split in a different number of quantization intervals at higher quantization rate.
At least one of the first and second bit-streams generated by an embedded quantizer
may be generated by non-uniform embedded quantizer. At least one of the first and
second bit-streams generated by a non-uniform embedded quantizer may be generated
by a non-uniform embedded dead zone quantizer. At least one of the first and second
bit-streams generated by a non-uniform embedded dead zone quantizer may be generated
by a non-uniform embedded double dead zone quantizer.
[0028] At least one of the first and second bit-streams generated by an embedded quantizer
may be generated by a uniform embedded quantizer. At least one of the first and second
bit-streams generated by a uniform embedded quantizer may be generated by a uniform
embedded dead zone quantizer. At least one of the first and second bit-streams generated
by a uniform embedded dead zone quantizer may be generated by a uniform embedded double
dead zone quantizer.
[0029] Each bit-stream is generated by an embedded quantizer.
[0030] The dequantizing means may comprise at least three levels, preferably more than seven
levels, and still more preferred more than ten levels.
[0031] A device according to the present invention may be located in a node of a telecommunications
network.
[0032] The present invention also provides two or more signals generated by any of the methods
of described above
[0033] The present invention furthermore provides a telecommunications network comprising
a device according to the present invention and as described above. The present invention
also includes a software product such as a computer program product, which when executed
on a computing device executes any of the methods of the present invention. The present
invention also includes this software product stored on a signal medium such as an
optical or magnetic disk or a magnetic tape or similar. The quantizers according to
the present invention may have one or more of the following properties
1. Multiple Description Scalar Quantizers are provided for communication systems using
diversity to overcome channel impairments. The Multiple Description Scalar Quantizers
are Embedded. Hence, the name Embedded Multiple Description Scalar Quantizers.
2. The quantizer corresponding to the central channel can be embedded uniform with deadzone. This design propriety enables EMDSQ to outperform the state of the art
3. For example, the deadzone can be equal to the uniform partitions resulting in a
uniform quantizer.
4. Or alternatively, the deadzone can be the double of the uniform partitions resulting
in a double deadzone uniform quantizer.
5. The design of EMDSQ allows construction of embedded side quantizers with the following
propriety. two partition cells at one quantization level can be divided into a different
number of partitions at a higher quantization level.
6. An EMDSQ according to the present inventioncan possess a redundancy control mechanism for each quantization level. This is an extra feature from the previous overall control
of redundancy
[0034] These and other characteristics, features and advantages of the present invention
will become apparent from the following detailed description, taken in conjunction
with the accompanying drawings, which illustrate, by way of example, the principles
of the invention. This description is given for the sake of example only, without
limiting the scope of the invention. The reference figures quoted below refer to the
attached drawings.
Brief Description of the drawings
[0035]
Fig. 1A illustrates the basic principle of multiple description coding using classical
fixed-rate scalar quantizers.
Fig. 1B illustrates an example of multiple description coding using classical fixed-rate
scalar quantizers in which the partition-cells of the central quantizer are obtained
by intersecting the partition cells of the two side quantizers.
Fig 2A illustrates two-channel EMDSQ according to an embodiment of the present invention.
the side quantizers are Q
, with the number of side quantizers being m = 1,2, and there being two quantization levels p=0,1. Q
(x) represents the central quantizer. Neglecting the signs, the side and central quantization
intervals are of the form S
, S
and C
, C
, respectively
Fig 2B illustrates four-channel EMDSQ according to an embodiment of the present invention:
the side quantizers are Q
with the number of side quantizer being m=1...4, and there being two quantization
levels p = 0,1. The central quantizer is Q
Fig. 3 is an illustration of redundancy ρ versus number of channels for 2≤M≤7 in function of a quantization level p, where the total number of quantization levels
is P=5, and 0≤p≤5.
Fig. 4 is a four-level representation of a first side quantizer Q
for two-channel EMDSQ for an example with granular region ranging from 0 to 23.
Fig. 5 illustrates a comparison of side and central rate-distortion performance between
EMDSQ and MDUSQ
Fig. 6 illustrates a comparison of side and central rate-distortion performance obtained
on a "Lena" image with a resolution of 512x512 pixels with an MD-QT code employing
EMDSQ according to an embodiment of the present invention and MDUSQ according to the
prior art respectively.
Fig. 7 illustrates performance (PSNR in dB) of the central reconstruction of MD-QT
coding based on EMDSQ according to an embodiment of the present invention compared
to the one based on MDUSQ for bit rates ranging from 0.125 to 4 bpp.
Fig. 8 illustrates a transmission system according to an embodiment of the present
invention, with at the transmitter side a plurality of quantizers for generating with
different quantizations, from a source digital signal, a plurality of bit-streams,
and with at the receiver side a plurality of dequantizers for generating, from at
least partially received bit-streams, a plurality of inverse quantized bit-streams
which may be combined to obtain a better approximation of the source signal.
Fig. 9 illustrates a transmission system according to another embodiment of the present
invention, with at the transmitter side a quantizer for generating with different
quantizations, from a source digital signal, a plurality of bit-streams, and with
at the receiver side a combined central dequantizer for generating, from at least
partially received bit-streams, a combined inverse quantized bit-stream.
Fig. 10 illustrates an EMDSQ with connected partitions cells and the corresponding
embedded index assignment strategy for two quantization levels (P=1).
Fig. 11 illustrates recursive block-matrix decomposition for each quantization level
q, 0≤q≤K.
Fig. 12 illustrates redundancy ρ versus quantization level q,0≤q≤5 for(a) Lq=3, L
-3 ≤ Nq ≤ L
, (b) 2 ≤ Lq ≤ 5 , Nq = L
in accordance with an embodiment of the present invention.
Fig. 13 shows an EMDSQ index assignment strategy for (b) one and (c) two quantization
levels employing disconnected partition-cell high-rate quantizers according to an
embodiment of the present invention.
Fig 14 shows a comparative central-channel rate-distortion performance for EMDSQ,
without disconnected partition-cells and with one (K = 0), two (k = 1 ) and three (K=2) quantization levels with disconnected partition-cell quantizers
according to embodiments of the present invention.
Fig. 15 and 16 show implementations of embodiments of the present invention in computers
and embedded processors.
Acronyms
[0036]
EMDSQ : Embedded Multiple Description Scalar Quantizers
MDC: Multiple Description Coding
MDSQ. Multiple Description Scalar Quantizers
MD-QT: Multiple Description-Quad Tree
MDUSQ Multiple Description Uniform Scalar Quantizers
PDF: probability density function
PSNR peak signal to noise ratio
SDC: Single-Description Coder
Description of the illustrative embodiments.
[0037] The present invention will be described with respect to particular embodiments and
with reference to certain drawings but the invention is not limited thereto but only
by the claims. The drawings described are only schematic and are non-limiting. In
the drawings, the size of some of the elements may be exaggerated and not drawn on
scale for illustrative purposes. Where the term "comprising" is used in the present
description and claims, it does not exclude other elements or steps.
[0038] Furthermore, any terms such as first, second, third and the like in the description
and in the claims, are used for distinguishing between similar elements and not necessarily
for describing a sequential or chronological order It is to be understood that the
terms so used are interchangeable under appropriate circumstances and that the embodiments
of the invention described herein are capable of operation in other sequences than
described or illustrated herein.
[0039] The present invention relates to data communication, more particularly to transmission
of multiple bit-streams over a channel or over a plurality of channels, whereby each
bit-stream in itself can reconstruct an approximation of the original data, for example
an approximation of the original image if the source data is image data. Hence, the
present invention does not require that all digital streams are used to create the
original signal at a receiver However, for a dispersive or noisy environment, the
more bit-streams that are received and combined with each other, the better the reconstructed
data, e.g. image is likely to be. Each, or at least a plurality, of the bit-streams
are quantized in a different way. The process of the present invention is illustrated
in Fig. 8 and in Fig 9. The inverse quantization, that is dequantization may be done
in separate quantizer for each bit stream or in a single quantizer for all the streams.
[0040] At the sender or transmitter side of a transmission system, or at any intermediate
part or node of the system where quantization is required, a source digital signal
S, such as e.g. a source video signal (an image), or more generally any type of input
data to be transmitted, is quantized in a quantizer Q, or in a plurality of quantizers
Q
1, Q
2, ..., Q
N, so as to form a number of N bit-streams S
1, S
2, .. , S
N. The source signal can be a function of one or more continuous or discrete variables,
and can itself be continuous or descrete-valued. The generation of bits from a continuous-valued
source inevitably involves some form of quantization, which is simply an approximation
of a quantity with an element chosen from a discrete set. Each of the generated N
bit-streams S
1, S
2, .., S
N may or may not be encoded subsequently, for example, entropy encoded, in encoders
C
1, C
2, ..., C
N before transmitting them over a channel ≈ An encoder produces from the source signal
a signal which is compatible with the channel. The channel is the physical medium
that conducts the transmitted signal. After transmission over the channel the signals
are received at a receiver or decoder side. A receiver or decoder attempts to recreate
the message from the received signals. The received signals may be distorted or include
deletions (e.g. caused by interference). The at least partially received signals P
1, P
2, ..., P
N are inverse quantized or dequantized at the receiver side of the transmission system.
The terms "inverse quantizing" and "dequantizing" have the same meaning, and one can
be replaced by the other in the present document. The inverse quantization or dequantizing
may be done in a separate dequantizer Q
1-1, Q
2-1, ..., Q
N-1 for each bit-stream or in a single dequantizer for all the streams Each inverse quantized
signal can be used alone for displaying an approximation of the source digital signal,
e.g. for displaying an approximation of a source image. Alternatively, at least two
inverse quantized signals may be combined into an inverse quantized and combined signal
which can be used e.g. for displaying a better approximation of the transmitted image.
The inverse quantization or dequantizing may be done in a combined inverse quantizer
with more than two quantised signals, also leading to an inverse quantized and combined
signal which can be used e.g. for displaying the transmitted image
[0041] For the two-channel case, the basic principle of multiple description coding using
classical fixed-rate scalar quantizers is illustrated in Fig. 1A. At the sender site,
the input source is quantized using two different scalar quantizers
Q1 and
Q2 , producing two different description of the input source, which are sent to the
client over two different channels. If only one description is received at the client
side, depending on the received description, the decoder reconstructs an approximation
S1 or
S2 of the input source using the inverse quantizers (dequantizers)
Q or
Q. If both descriptions are received, the decoder reconstructs a different version
Sc of the input source using the inverse quantizer
Q. As shown in the example of Fig. 1B, the partition-cells of the central-channel quantizer
Qc are given by intersecting the partition-cells of the side-quantizers
Q1 and
Q2 . Hence, the central-channel reconstruction
Sc is better (in distortion sense) than any of the side-channel reconstructions
S1 or
S2. It is important to remark that multiple-description coding using scalar quantizers
illustrated by Fig 1A and 1B refers to fixed-rate (single-rate) quantizers. The present
invention focuses on
embedded side and central-channel quantizers, as discussed next.
[0042] Figs. 2A and Fig. 2B illustrate examples of embedded quantizers in accordance with
the present invention. For the two-channel case, it is noticeable from Fig. 2A that
both the side quantizers
Q,
Q as well as the central-channel quantizer
Q at level 0 are finer than the corresponding quantizers at level 1,
Q,
Q and
Q respectively. Similarly, for the four-channel case shown in Fig. 2B, the side quantizers
Q,
Q Q,
Q as well as the central-channel quantizer
Q at level 0 are finer than the corresponding quantizers at level 1,
Q,
Q,
Q,
Q and
Q respectively. This example illustrates that both the side quantizers as well as the
central quantizers are embedded, that is, the partition cells at a given quantization
level are embedded in the partition cells at all the higher quantization levels.
[0043] For the quantizers of the present invention, EMDSQ, according to an embodiment the
side quantizers
Q are non-uniform embedded quantizers, thus for any
0 ≤ p ≤ P there exist
k,j, k ≠ j such that
Lk ≠ Lj. . The example depicted in Fig 2A illustrates an instantiation of a two-channel EMDSQ
according to the present invention In view of simplification, only two quantization
levels p=0,1 are considered. It is noticed for instance that the quantization intervals
S and
S of the second-channel embedded quantizer
Q are divided respectively into three quantization intervals
S,
S and
S of the higher rate quantizer
Q. On the contrary, the dead zone
S of the second-channel embedded quantizer
Q is not divided and is transformed into
S of
Q.
[0044] A uniform entropy-coded scalar quantizer is optimal for high rates, and nearly optimal
for lower rates, as described in D Taubman and M W. Marcellin,
JPEG2000 - Image Compression: Fundamentals, Standards and Practice, Hingham, MA: Kluwer Academic Publishers, 2001. Furthermore, the above book also describes
that, for input data with symmetric probability density function (PDF), the rate-distortion
behaviour at low rates can be improved by widening the quantization interval located
around zero, that is, by using deadzone uniform scalar quantizers. The rate-distortion
function gives the minimum rate needed to approximate a source signal up to a given
distortion. It can be noticed that the central quantizer
Q and
Q obtained from the side quantizers
Q,
Q and
Q,
Q presented in Fig. 2A is a double-deadzone embedded quantizer, i.e. a quantizer having
equal quantization intervals with a size or width Δ, except for the quantization interval
around zero which has a size or width 2Δ. Hence, it shows the above-mentioned characteristics
of improved rate-distortion behaviour.
[0045] For two-channel EMDSQ, an analytical expression of an embodiment of a proposed embedded
side-quantizer for the first channel is:
where:
[0046] The boundary points in Eq. (1) are defined as follows.
[0047] In the above equations and formulae:
└a┘ denotes the integer part of a ,
Δ > 0 is the size or width of a quantization interval for Q
,
p%2= p-2 ·└p/2┘, and
ξ (with ξ <1) determines the size or width of the deadzone.
[a, b) denotes an interval which is closed in a but open in b, that is if x ∈ [a,
b) then a ≤ x <b
The index
k ∈Z+ determines the size or width of the quantizer granular region, which is the interval
[y
k-Δ/2, y
k-Δ/2]; source samples in this interval will be approximated within ± Δ/2 by their
quantized values.
[0048] Since the parameter ξ controls the size or width of the central deadzone, the central
deadzone being one of the quantizer intervals by definition, by tuning its value,
corresponding families of embedded quantizers may be obtained. It should be noted
that, when ξ= 1/2, the central quantizer is uniform, while when ξ=0, the deadzone
width is 2Δ; this is the case exemplified in Fig. 2A. Negative values of the parameter
ξ are further widening the deadzone, as described in the JPEG2000 book mentioned above.
Generalisation of the invention to M channels EMDSQ
[0049] M channel quantizers can only be formulated analytically, since it is not possible
to graphically build an M-dimensional matrix to apply Vaishampayan's method.
[0050] Taking as a starting point equation Eq. (1) that describes an embodiment of the first
channel quantizer corresponding to the two-channel EMDSQ, it is possible to generalise
the analytical formula so as to obtain an embodiment for
M-channels, as shown below:
with.
and the boundary points are defined as follows:
where
m,1 ≤
m ≤
M denotes the channel index.
[0051] It is to be noted that the particular example of Eq. (1) is derived from Eq. (4)
for
M=2,
m=1 and ξ=0.
[0052] Based on the expressions for
A,
B,
A,
B given above, one notices that the size or width Δ
(p) of a quantization interval for the side quantizer
Q at level
p and index
m depends on the number of channels
M by Δ
(p)=
MpΔ(0), where Δ
(0) is the size or width of the quantization interval for the highest-rate side quantizer
Q, and Δ
(0)=
mΔ or Δ(0) =(
M+1-
m)Δ
[0053] Fig. 2B depicts the case of four channels (
M=4) and two quantization levels ( 0 ≤
p ≤ 1 ) It is to be noted that the quantization intervals of the side quantizers
Q, 1 ≤
m ≤ 4 are embedded respectively in the quantization intervals of the side quantizers
Q. It is also to be noted that the central quantizer
Q is a double deadzone embedded quantizer with quantization interval size or width
Δ
=4
pΔ
, where
Δ= Δ is the quantization interval size or width of
Q . The negative side of the quantizers is not illustrated, but is a mirrored version
of the positive side which is shown.
Dependency between redundancy and the number of channels
[0054] All approaches that imply MDC involve creating redundancy in the bit-stream transmitted
over several channels. By
Rm,1≤
m ≤
M the rates are denoted, and by
Dm(Rm) the corresponding side average distortions over
M channels. The average distortion of the central quantizer shall be
D0. The standard source coder, i.e. the single-description coder (SDC), a coder that
implies one source coder and one decoder contrary to MDC which implies multiple source
encoders and multiple source decoders, minimises
D0 for a given rate
R0. Intuitively, the redundancy is the bit-rate sacrificed compared to the SDC coder
in order to lower the
Dm distortion A redundancy function is considered:
where
R0 is the lowest rate needed by any SDC in order to achieve the central
D0 distortion of the MDC. For a fixed
D0, the redundancy ranges from
(M - 1)
R0 (the bit-stream is replicated over the
M channels) to 0 (the data is totally uncorrelated over the
M channels).
[0055] For the lowest-rate case (see example of Fig. 2B), the number of central quantizer
quantization intervals is 2(
M+i)-1. Hence, the central quantization rate is R
0=log
2(2(
M+1)-1). Since the number of quantization intervals for all lowest-rate EMDSQ side-quantizers
is three, their individual rate is
Rm = log
2 3 . Thus, formula Eq. (6) for the lowest rate quantizers can be written ρ
p=
M log
23-log
2(2
M+1). Similarly, for level
p=P-1
, the number of quantization intervals of the side quantizers
Q is 4
M-1, which yields a rate of
Rm = log
2(4
M-1). The central quantization rate will be
R0 =(log
2 2
M(
M+1)-1). Following the same reasoning, for quantization level
p,
Rm=log
2(4
MP-P-1) and
R0 = log
2(2
MP-P (
M + 1)-1) are obtained. Consequently, the redundancy for quantization level
p can be expressed as follows:
[0056] From Eq. (7), one can deduce the analytical expression of the normalised redundancy:
[0057] One can conclude that for the EMDSQ the redundancy is directly dependent on the number
of channels. Whereas, in the case of two channels, one can trigger the redundancy
level by the number of diagonals filled in the index assignment matrix as described
in V. A. Vaishampayan, "Design of multiple description scalar quantizers,"
IEEE Trans. Inform. Th., vol. 39, no. 3, pp. 821 - 834, 1993.
[0058] A graphic representation of the redundancy versus the number of channels, given by
Eq (8), is shown in Fig. 3. The theoretical boundary of the redundancy (
M-1)
R0 is reached when the stream is replicated over
M channels and is represented by the upper curve in the graph. It is noticeable that
the redundancy between the channels monotonically decreases as the quantization level
p increases.
Coding scheme
[0059] The use of the EMDSQ according to the present invention into a wavelet-based coding
scheme is illustrated, for the particular case of the number of channels being M =
2. A proposed MD-QT coding system encodes the quantizers' output by using a customised
version of the wavelet-based QT coding of the significance maps algorithm described
in A. Munteanu, J. Cornelis, G. Van der Auwera, and P. Cristea, "Wavelet-based lossless
compression scheme with progressive transmission capability,
Int. J. Imaging Systems and Tech., vol. 10, no. 1, pp. 76-85, Jan. 1999. This is only one example of one particular
coding algorithm that can used EMDSQ. Any type of coding algorithm, and any type of
input source such as for example special domain, wavelet transform or DCT transform,
can be used.
Significance map coding
[0060] By
TP is denoted the significance threshold from a coding step corresponding to the quantization
level
p, 0
≤ p ≤P ; the significance of wavelet coefficients being recorded in a significance map with
respect to the applied threshold
TP By
k=(k1,k2) the spatial location of the wavelet coefficient from the wavelet transform matrix
is denoted, where
k1 and
k2 stand for the row and column index, respectively. By
Q(k, v) a quadrant with top-left co-ordinates
k=(
k1,
k2) and size or width
v=(ν
1,ν
2) is denoted, where ν
1 and ν
2 represent the quadrant width and height respectively. In view of simplification identical
power-of-two quadrant dimensions ν
1 and ν
2 are assumed, i. e. ν
1 = ν
2 = 2
J for some
J. The corresponding quadrant delimiting binary elements in the significance map p
is denoted by
Q (
k,
v) . The wavelet image
w=Q(
0,
V) is a matrix of
V1 ×
V2 elements, with
0= (0,0),
V =(V1,V2). For any wavelet coefficient, its absolute value and sign are denoted as
w(
1) and
s(
1) respectively, where
1=(
l1,
l2) with
0 ≤ l1 ≤ V1 and 0 ≤
l2 ≤
V2.
[0061] The significance of the wavelet coefficients from any
Q(
k,v)(∈
W,
v≠(1,1) with respect to the applied threshold
TP is recorded in
Q(
k,
v) and is determined via the operator
σp :
[0062] It is to be noted that the significance operator
σp determines the significance of a quadrant but not the significance of a coefficient.
For an individual wavelet coefficient the significant operator
σP is no longer applied, and instead, the quantizer index allocation operator, denoted
by δ(
w(
1)), is utilised.
[0063] The EMDSQ by their structure present the particularity that different quantization
intervals at quantization level p are divided into different numbers of quantization
intervals at the quantization level
p-1 as shown hereinabove. Thus, it can be deduced that in order to perform the index
allocation, the wavelet coefficients have to be compared against the values of the
boundary points of quantization intervals at a certain quantization level p. It is
considered that an arbitrary quantization interval at level p will be divided into
N quantization intervals at level
p-1 The index allocation operator δ determines the codeword associated to each quantized
coefficient as follows:
where the boundary points are denoted as
Tδ,n with 0 ≤
n ≤
N and
Tδ,0 <
Tδ,1 Tδ,N. The manner in which the threshold
Tp and boundary points
Tδ,n are computed will be described below.
[0064] For the first quadtree-partitioning pass, as described in A. Munteanu, J. Cornelis,
G. Van der Auwera, and P. Cristea, "Wavelet-based lossless compression scheme with
progressive transmission capability,
Int. J. Imaging Systems and Tech., vol. 10, no. 1, pp. 76-85, Jan 1999, the significance of the wavelet image w is tested
with respect to the threshold
TP. If
σp(
W)=1, the significance map
Q(
0,V) of the wavelet image
w is split into four quadrants
Q(
ki,
V/2), 1≤
i≤4, each having half the original parent size or width, with
ki indicating the origin of each quadrant. The descendent significant quadrants are
then further spliced until the leaf nodes (i.e wavelet coefficients) are isolated.
For the leaf nodes, the symbols
Sn (0 <
n ≤
N ) are allocated by applying the index allocation operator δ(
w(
1)) . Thus, the significance pass records the positions
1 of all the leaf nodes newly identified as significant, using a recursive tree structure
of quadrants (or a quad-tree structure)
[0065] Once the positions and the corresponding symbols of the significant leaf nodes are
encoded during the significance pass,
p is set to
P-1 . Next, the significance pass is restarted to update the entire quad-tree structure
by identifying the new significant leaf nodes During this stage, only the significance
of the previously non-significant nodes and quadrants, i.e. those for which
δ(w(1))=
S1, and σ
P+1(Q(
k,v))=0 respectively, is encoded, and the significant ones are ignored since the decoder
has already received this information. Subsequently, the corresponding refinement
pass is activated for the significant leaf nodes. The refinement pass is performed
with respect to the corresponding refinement threshold
T. The described procedure is repeated, until the complete wavelet image is encoded,
i.e.
p=0, or until the target bit-rate is met.
Coding algorithm
[0066] The manner in which the significance thresholds, refinement thresholds and boundary
points are computed, is illustrated, for the particular case of the number of channels
being M = 2 .
[0067] As explained before, the coding passes performed by the proposed MD-QT coding system
are the significance pass, employing the significance thresholds
Tp,m , 0
≤ p ≤ P , followed by the refinement pass, utilising the refinement thresholds
T, with
m, 1
≤ m ≤ 2 denoting the channel index for the case with two channels.
[0068] For the lowest quantization rate
P , the starting thresholds corresponding to each channel are
TP,1 =
2T and
TP,2 = respectively. Since it is not desirable that the quantizer is characterised by
an overload region, or an unbounded interval, the
T value is related to the highest absolute magnitude
Wmax of the wavelet coefficients as
[0069] Hence, the maximum number of quantization levels is P=└log
2(
wmax/3)┘+1. In general, excepting the lowest quantization rate P , the significance thresholds
used for each channel
m ,
l ≤
m ≤ 2 are given by:
with
P-x= p, and x ≥1 The values
Tm are of the form
T1 = 2T and
T2 =4T respectively
[0070] Fig. 4 depicts the first channel EMDSQ with granular region ranging from 0 to 24
(x ∈ [0,24)). The significance map coding is performed with respect to the set of
thresholds
Tp,1 with the rate of decay given by Eq. (12). For the two-channel EMDSQ case, except
for the highest quantization rate
P, the description of the quantizers reveals that half of the quantization intervals
at level
p are divided into three quantization intervals at level
p-1, while the other half are not divided. Thus, three index allocation operators are
considered In the case
p=
P, the index allocation operator α(
w(
1))is used to assign for the leaf-nodes in the quadtree the symbols
Sα,1 and
Sα,2 as follows:
where
T =
TP,m and
T= 3
T.
[0071] In the case
p < Ptwo operators β(
w(
1)) and γ(
w(
1)) are considered, one for each of the two quantization interval types. For the quantization
intervals that are divided in three, the index allocation operator β(
w(
1)) is expressed as:
where the relations between the corresponding quantization interval boundary points
are
T =
T + Δ
,
T =
T+3·Δ
and
T =
T +4·Δ
, where
T = ((
x+
m)%2)2Δ
, x ≥ 1.
[0072] Apart from this, for the remaining half of the quantization intervals that are not
divided only one symbol
Sγ,1 is assigned through the index allocation operator γ(
w(1)) as follows:
[0073] The relation between the corresponding quantization interval boundary points is
T =
T +2Δ
, where
T = ((x+m+1)%2)4Δ
[0074] The purpose of the refinement pass is to perform the index allocation for coefficients
that have already been coded as significant at the previous significance passes. The
index allocation is performed with respect to the new updated values of the boundary
points. In order to apply the index allocation, the coefficient that must be refined
has to be rescaled with respect to the refinement pass threshold
T given by:
[0075] In order to improve the compression results, the output of the MD-QT coder (significance
symbols, quantizer index symbols, signs symbols) may further be entropy coded with
an adaptive arithmetic coder, as described in I. H. Witten, R. M. Neal, and J. G.
Cleary, "Arithmetic coding for data compression," Communications of the ACM, vol.
30, no. 5, pp. 520-540, June 1987, that uses four different probability models. One
model is used to encode the quadrant significance symbols. Another model is used for
the sign symbol encoding. Finally, another two models are utilised to entropy code
the symbols generated by the index allocation operators α(
w(
1)) and β (
w(
1)) respectively. Since the MD-QT output for the quantization intervals that are not
divided is represented by only one symbol S
γ,1, it is completely redundant to further encode these symbols.
EXPERIMENTAL RESULTS
[0076] To perform a comparison between the EMDSQ according to the present invention and
MDUSQ as described in Guionnet et al., both quantizers are applied on a memoryless
Laplacian source of a 256x256 matrix of Laplacian random generated numbers with zero
mean and σ=14.6, simulating a wavelet subband. Fig. 5 shows that comparable results
are obtained for the side channel(s) and that the EMDSQ of the present invention outperforms
MDUSQ for the central channel. Similar experimental results were obtained varying
the standard deviation within the range 12<σ<90 .
[0077] Similar to EMDSQ, the MDUSQ has been integrated in the MD-QT coding scheme, resulting
into a common entropy-coding module for both types of quantizers. The results shown
in Fig. 6 obtained on the Lena image reveal that on the central channel the EMDSQ
outperforms MDUSQ with 0.52-1.08 dB Similarly, the results obtained on a common image
data set given in the Table of Fig. 7 show that in comparison to the prior art MDUSQ,
the EMDSQ of the present invention provides constantly better rate-distortion performances
on the central channel for all the rates. In particular, the quantizers of the present
invention can provide under certain circumstances at least 1% improvement of the dB
of peak signal to noise ratio of data processed in accordance with the present invention.
Controlling redundancy
[0078] In order to reduce bandwidth it would be preferable to reduce any redundancy in transmitted
signals. In accordance with an aspect of the present invention the level of redundancy
can be adapted depending upon the channel. The embedded bitstreams made by such quantizers
are preferably progressively refinable. In accordance with an aspect of the present
invention, the redundancy in information is controlled between descriptions on a level-by-level
basis, for example at each level. Thus, the present invention provides an embedded
quantizer having means for controlling the amount of redundancy between different
descriptions at at least one quantization level
[0079] The embedded multiple description scalar quantizers proposed above according to the
other embodiments of the present invention are quantizers with connected partitions
cells that target a high redundancy level and provide good coding results. In an EMDSQ
in accordance with further embodiments of the present invention such quantizers can
be successfully employed for the coarser quantization levels for an increased resilience
of the multiple descriptions. On the other hand quantizers with disconnected partition
cells can be employed in order to reduce the descriptions' redundancy. Hence, for
the less important layers (corresponding to the finer quantization levels), embedded
side quantizers with disconnected partition cells producing double-deadzone central
quantizers can be designed. One aspect of the present invention is the solution to
this problem and the mixture between these two classes of quantizers, yielding an
EMDSQ family.
[0080] For the two-channel EMDSQ, the set of embedded side-quantizers are denoted as
Q=,...,
Q,
Q,...,
Q, with
m = 1,2 , where the quantization level
q, K+1
≤ q ≤ K +
P + 1
, corresponds to the low-rate quantizers with connected partitions cells, while
q, 0≤q≤K corresponds to the higher-rate quantizers with disconnected partitions cells In these
notations
P+1 and
K+1 denote the number of quantization levels for the embedded quantizers with connected
and disconnected partition cells respectively. Also,
Q,...,
Q,
Q,...,
Q denote the set of embedded central-quantizers
Q(
q,
q)=
Q(
q)I
Q(
q) for any quantization level
q, 0 ≤ q ≤ K +
P + 1
.
[0081] From the analytical expression of the embedded multiple-description scalar quantizers
with connected partitions cells described above one can derive the following index
allocation matrix:
where 1≤r≤3N, 3N represents the number of partition cells contained in the granular
region of the central quantizer at the quantization level
q=
K+1, and P=└log
2 N┘.
[0082] In the EMDSQ according to the present embodiment, the integer entries in the index
allocation matrix
I(
r) of Eq. 16 are replaced by
S×S square matrices of consecutive indices
Ar=(α
ij)
l≤i,j≤S (see Fig. 10). In this generic case, the index allocation matrix is given by:
[0083] For any matrix
M we define the operator
nnz(
M) that determines the number of nonzero elements contained in the matrix M . From
Eq. 17 it follows that for the central quantizers at level
q=
K +1 the sizes of the bounded partitions cells are of the form
nnz(Ar)·ΔC , where Δ
C ∈
i + is the central-channel's step size at the highest rate. Imposing the design constraint
of obtaining a double-deadzone central quantizer for the level
q =
K + 1 implies equal size for all bounded partition-cells. This necessarily implies an
equal number of nonzero elements for all the index matrices
Ar, i.e.
nnz(Ar)=const,∀r, 1 ≤
r ≤ 3N. Therefore, the cell size for the central quantizer at level
q=K+1 is Δ
=
nnz(Ar)ΔC
[0084] From the above and the EMDSQ cell size formulas (Eq. 1-3 above) it can be deduced
that the central channel quantizer is a double-deadzone embedded quantizer with the
cell size of the form:
for any level
q, K + 1
≤ q≤ K +
P +1 . Consequently, from the above, one can deduce that the cell size for the side channels
is of the form Δ
(q) = 2
q-K-1 Δ
(K+1) where Δ
(K+1) = nnz(
Ar)ΔC or Δ
(K+1) =2.
nnz(
Ar)Δ
C
[0085] The example depicted in Fig. 10 illustrates an embodiment of the EMDSQ with connected
partitions cells for two quantization levels and the corresponding embedded index
assignment strategy. The negative side of the quantizers is a mirrored version of
the positive side shown in Fig. 10. If
nnz(Ar) is constant, then
Q0C and
Q1C, are double-deadzone scalar quantizers .
[0086] Starting with the quantization level g=k , quantizers with disconnected partition
cells are employed in order to reduce the redundancy between the two descriptions.
This corresponds to a reduced error-robustness for the finer quantization levels;
however, this reduces the rate in comparison to the rate that would be obtained with
quantizers with connected partition cells.
[0087] At the level q
= K we consider each of the SxS square matrices A
r as block matrices of the form A
r = [
B]
1≤i,j≤LK defined by the contained blocks
B, 1
≤ i,j
≤LK and represented as follow
Moreover, each of the blocks
B are square matrices of the same size
SK =
S/
LK. Similarly, at the finer quantization level
q=
K-1
, each block matrix
B is again of the form.
B =[
B]
1≤m,n≤LK-1 for any 1≤
i,j≤
Lk, and the contained blocks
B are of the size
SK-1 =
S/
(LK .LK-1) Recursively, B
=[
B]1≤
m,n≤L
q-1 for any 1 ≤
i,j ≤
Lq, and for all the quantization levels
q, 0≤
q ≤
K (see Fig. 11).
[0088] From
nnz(A1) =
nnz(A2) =
= nnz(A3N)= const. and imposing the design constraint that for any quantization level one obtains a
double-deadzone central quantizer, yields:
nnz(B) =
nnz(B) ,
∀i,j,m,n 1
≤ i,j, m,n ≤ Lq for any [
B]≠[0] and [
B]≠[
0], where by [
0] one denotes the zero matrix.
[0089] Following the recursive decomposition of each block matrix
B, 1 ≤
i,j ≤ L
q+1, one obtains
L square blocks of size:
Notice that for the highest-rate quantization level q =0 all blocks
B 1≤
i,j ≤L
0 are matrices of dimension S
0 =1 , i.e. they contain a single element.
[0090] One obtains the cell size at any level
q,1 ≤ q ≤ K of the double-deadzone central quantizer by:
for any 1 ≤
i,j ≤
Lq and [
B]≠[
0].
[0091] Consider a block matrix
M=[
Mij]
1 ≤ i ≤ 1,1 ≤ j ≤ J. The number of blocks [
Mij]=[
0] contained in
M is determined via the nonzero-blocks operator nzb(
M,
Mij).The operator nzb(
M,
Mij) is similar to the operator
nnz(M) in the case of unitary size blocks
Mij . With this definition, for any of the block matrices
B=[
B]
1 ≤ m,n ≤ Lq-1, 1
≤i,j≤Lq, the number of blocks
B different from the zero matrix is given by
Nq-1 =
nzb(
B B). Also, we denote by
NK =
nzb(Ar,B) where
1≤i,j≤LK.
[0092] The total number of indices mapped in each
B block matrix at quantization level
q is
for any
r, 1≤
r≤3
N and
l≤
i,j≤
Lq. Moreover,
Therefore, the total number of indices mapped in the index assignment matrix
I(A
r) is
[0093] It can then be shown that the analytical expression of central EMDSQ for any quantization
level q, , 0 ≤
q ≤
K +
P + 1 is:
where the level function
l(q)=
q-K-1
, H(x) denotes the Heaviside unitary step function and
sign(x) = 2H (x) - 1
.
[0094] Denote by
Rm the rates and by
Dm(Rm) the corresponding side description distortion, where
m=1,2. Also, denote by
D0 the central distortion. The standard source coder, i.e. the single-description coder
(SDC) minimizes
D0 for a given rate
R0. Intuitively, the redundancy is the bit-rate sacrificed by an MDC compared to the
SDC in order to achieve the same central
D0 distortion:
One derives the redundancy expression for the quantization levels
q,K +1≤
q ≤ K +
P+1 and the SDC rate
R0 = log
2(3 . 2
K+P+2-q -1) and the corresponding side-channel rate is
Rm = log
2(2·2
k+P+ 2-q -1). Thus, formula 22 for
K +1
≤ q ≤ K +
P +1 is given by:
For the quantization levels
q,0 ≤
q ≤
K employing quantizers with disconnected partitions cells, the SDC rate is
R0 = log
2(3·2
P+1·Π
kk=qNk-1)and the corresponding side-channel rate is of the form
Rm = log
2(2·
2P+1ΠLk -1) Thus, formula 22 for 0 ≤
q ≤
K is:
From Eq. 10 one can deduce the analytical expression of the normalized redundancy:
One can conclude that for any embodiment of the present invention which is an instantiation
of the generic EMDSQ family, the redundancy is directly dependent on the quantization
level. In addition, for all the quantization levels
q,0≤
q ≤
K,the redundancy can be controlled via the
Lq and
Nq parameters, with
Nq ≤
L.
[0095] This mechanism is shown in Fig. 12 which depicts the normalized redundancy versus
the quantization level (as expressed by Eq. 25), for practical instantiations of the
Lq and
Nq parameters. It is noticeable that the descriptions' redundancy decreases from the
higher to the lower quantization levels, and moreover, by changing the parameters
Lq and
Nq we can speed the redundancy' rate-of-decay.
[0096] In order to demonstrate the redundancy control mechanism in accordance with the above
embodiments of the present invention the rate-distortion behavior for several instantiations
of the generic family of EMDSQ has been determined. The EMDSQ instantiations employ
one
(K = 0), two
(K = 1 and three
(K = 2) quantization levels with disconnected partition-cell quantizers. In all the
cases
Lq = 2 and
Nq = 4 for any
q,0 ≤ q ≤ K. The corresponding index assignment is illustrated in Fig. 13.
[0097] The EMDSQ instantiations have been applied on a memoryless Laplacian source of random
generated numbers with zero mean and σ = 44.7, modeling a wavelet subband.
[0098] Fig 14 shows that it is possible to speed the distortion's rate-of-decay for the
central channel by decreasing, after a quantization level, the redundancy obtained
by varying the standard deviation within a broad range of values (12 <σ< 90).
[0099] EMDSQ instantiations according to the present embodiment have also been incorporated
in a practical wavelet coding system that entropy codes the quantizer indices using
the QuadTree coding algorithm. The central-channel rate-distortion performances obtained
with the different EMDSQ instantiations have been applied on a common data set for
Lena and Goldhill images. The proposed EMDSQ family according to this embodiment allows
for controlling the redundancy between two descriptions at each quantization level
[0100] Fig. 15 shows the implementation of a coder/decoder which can be used with the present
invention implemented using a microprocessor 230 such as a Pentium IV from Intel Corp.
USA, e.g. in a Personal Computer. The microprocessor 230 may have an optional element
such as a co-processor 224, e.g. for arithmetic operations or microprocessor 230-224
may be a bit-sliced processor. A RAM memory 222 may be provided, e g. DRAM. Various
I/O (input/output) interfaces 225, 226, 227 may be provided, e.g DART, USB, I
2C bus interface as well as an I/O selector 228. These may serve to receive a source
digital signal. FIFO buffers 232 may be used to decouple the processor 230 from data
transfer through these interfaces. A keyboard and mouse interface 234 will usually
be provided as well as a visual display unit interface 236. Access to an external
memory such as a disk drive may be provided via an external bus interface 238 with
address, data and control busses. The various blocks of the circuit are linked by
suitable busses 231 1 The interface to the channel is provided by block 242 which
can handle the encoded signals as well as transmitting to and receiving from the channel.
Encoded data received by block 242 is passed to the processor 230 for processing.
[0101] Alternatively, the circuit of Fig. 15 may be constructed as a VLSI chip around an
embedded microprocessor 230 such as an ARM7TDMI core designed by ARM Ltd., UK which
may be synthesized onto a single chip with the other components shown. A zero wait
state SRAM memory 222 may be provided on-chip as well as an optional cache memory
224. Various I/O (input/output) interfaces 225, 226, 227 may be provided, e.g. UART,
USB, I
2C bus interface as well as an I/O selector 228. FIFO buffers 232 may be used to decouple
the processor 230 from data transfer through these interfaces. A counter/timer block
234 may be provided as well as an interrupt controller 236. Access to an external
memory may be provided an external bus interface 238 with address, data and control
busses. The various blocks of the circuit are linked by suitable busses 231. The interface
to the channel is provided by block 242 which can handle the encoded signals as well
as transmitting to and receiving from the channel. Encoded data received by block
242 is passed to the processor 230 for processing.
[0102] Software programs may be stored in an internal ROM (read only memory) 246 Software
programs for carrying out coding and/or encoding, especially the quantising and dequantising
in accordance with any of the methods of the present invention, including redundancy
control may also be stored on the system in executable form. In particular software
programs may be provided for quantising and dequantising as well as redundncy control
according to embodiments of the present invention described above to be applied to
blocks of data to generate two or more streams of encoded data. That is the software,
for executing on the processor 230 has code for carrying out the function of quantizing
a source digital signal to generate with different quantizations at least a first
and a second bit-stream, of which at least one bit-stream has been generated by an
embedded quantization, transmitting at least one of the at least first and second
bit-streams and generating a dequantized digital signal from at least parts of one
of the transmitted at least first and second bit streams, whereby if in the generation
of the dequantized digital signal the parts of the at least first and second bit-streams
are combined, the combined dequantized signal is generated by an embedded dequantizer
having at least two quantization levels and having at least one quantization interval
at each quantization level which is finer than quantization intervals for dequantizing
any of the at least first and second bit-streams. Further, code for redundancy control
may be provided.
[0103] Code may be provided so that each quantization level has a quantization rate and
at least one bit-stream generated by an embedded quantization is generated by an embedded
quantization where at least two quantization intervals at lower quantization rate
are split into a different number of quantization intervals at a higher quantization
rate. Code may also be provided so that at least one bit-stream generated by an embedded
quantization is generated by a non-uniform embedded quantization Code may also be
provided so that at least one bit-stream generated by a non-uniform embedded quantization
is generated by a non-uniform embedded dead zone quantization. Code may be provided
so that at least one bit-stream generated by a non-uniform embedded dead zone quantization
is generated by a non-uniform embedded double dead zone quantization. NCode may be
provided so that at least one bit-stream generated by an embedded quantization is
generated by a uniform embedded quantization. Code may be provided so that at least
one bit-stream generated by a uniform embedded quantization is generated by a uniform
embedded dead zone quantization. Code may also be provided so that at least one bit-stream
generated by a uniform embedded dead zone quantization is generated by a uniform embedded
double dead zone quantization. each bit-stream is generated by an embedded quantization.
[0104] The methods described above may be written as computer programs in a suitable computer
language such as C and then compiled for the specific processor in the design. For
example, for the embedded ARM core VLSI described above the software may be written
in C and then compiled using the ARM C compiler and the ARM assembler. Reference is
made to "ARM System-on-chip", S. Furber, Addison-Wiley, 2000 The present invention
also includes a data carrier on which is stored executable code segments, which when
executed on a processor such as 230 will execute any of the methods of the present
invention, in particular will execute quantising and/or dequantising as well as redundancy
control according to embodiments of the present invention described above to be applied
to images The data carrier may be any suitable data carrier such as diskettes ("floopy
disks"), optical storage media such as CD-ROMs, DVD ROM's, tape drives, hard drives,
etc. which are computer readable.
[0105] Fig. 16 shows the implementation of a coder/decoder which can be used with the present
invention implemented using an dedicated quantiser/dequantiser module. Reference numbers
in Fig 16 which are the same as the reference numbers in Fig 10 refer to the same
components - both in the microprocessor and the embedded core embodiments.
[0106] Only the major differences in Fig. 16 will be described with respect to Fig. 15.
Instead of the microprocessor 230 carrying out methods according to the present invention
this work is now taken over by a quantiser/dequantiser module 240 Module 240 may be
constructed as an accelerator card for insertion in a personal computer The module
240 has means for carrying out signal coding and/or decoding according to embodiments
of the present invention described above. These coders and encoders may be implemented
as a separate module 241, e.g. an ASIC (Application Specific Integrated Circuit) or
an FPGA (Field Programmable Gate Array) having means for quantising and/or dequnatising
according to embodiments of the present invention.
[0107] Similarly, if an embedded core is used such as an ARM processor core or an FPGA,
a module 240 may be used which may be constructed as a separate module in a multi-chip
module (MCM), for example or combined with the other elements of the circuit on a
VLSI. The module 240 has means for carrying out quantising and/or dequantising according
to embodiments of the present invention. As above, these qunatisers/dequantisers may
be implemented as a separate module 241, e g. an ASIC (Application Specific Integrated
Circuit) or an FPGA (Field Programmable Gate Array) having means for quantising and/or
dequantising according to embodiments of the present invention described above.
[0108] While the invention has been shown and described with reference to preferred embodiments,
it will be understood by those skilled in the art that various changes or modifications
in form and detail may be made without departing from the scope and spirit of this
invention